A ray of
light passing through the point (1, 2) reflects on the *x*-axis
at point A and the reflected ray passes through the point (5, 3).
Find the coordinates of A.

Let the
coordinates of point A be (*a*, 0).

Draw a
line (AL) perpendicular to the *x*-axis.

We know that angle of incidence is equal to angle of reflection. Hence, let

∠BAL
= ∠CAL = *Φ*

Let ∠CAX
= *θ*

∴∠OAB
= 180° – (*θ*
+ 2*Φ*) = 180°
– [*θ* + 2(90°
– *θ*)]

= 180° – *θ*
– 180° + 2*θ*

= *θ*

∴∠BAX
= 180° – *θ*

From equations (1) and (2), we obtain

Thus, the coordinates of point A are.

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